I am visiting Taiwan from 7/23 to 7/30 with my wife and 2 daughters(22 & 16).

From the data I have checked, it will rain heavily during July 23rd to July 30th. The temperature will be 75F to 90F at that time. The typhoon will happen frequently in that period. It will influence the sightseeing a lot. You are advised to rearrange your schedule, may be you can visit there in May or June.